You don't "need" wet/dry biofilters, and you really don't "need" live rock either. They are not requirements like oxygen is. However they are backups, which always are working, especially on ammonia, and they are also always working in-between scrubber cleanings. Without LR or sand, or without a bio filter, you would need to pay special attention to always having lots of algae growth on at least one scrubber screen when you cleaned another screen. And most people don't have more than one screen, so there is no option. Also if something happened to your scrubber growth, you'd be in trouble while waiting for new growth to occur.
The wet/dry is a powerful ammonia remover, but if you have lots of sand you should be ok without it. A wet/dry (also called an ammonia tower when built large enough) is most useful in retail where the tanks have no rock or sand. Wet/dry's do makes lots of nitrate, and do nothing for phosphate. LR and deep sand beds do handle some nitrate, but do nothing for phosphate (except become a temporary sponge for it). Skimmers and GAC don't remove any ammonia at all.
So there is no biological need for a wet/dry or for rock/sand, but you will probably always want one or the other.